Math Answers

2. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

The scores of all pro golfers for a course are normally distributed with the mean of 70 and a standard deviation of 3. Suppose 36 pro golfers played the course today. Find the probability that the mean score of the 36 pro golfers exceeded 71.

Show, by the use of the truth table (truth matrix), that the (p v q) v [(¬p) ʌ (¬q)]  is a contradiction. 

Show that ¬p →(q → r) and q → (p V r) are logically equivalent.

Use row reduction algorithm to solve the following system of equations.

x1 − 7x2 + 6x4 = 5

x3 − 2x4 = −3

−x1 + 7x2 − 4x3 + 2x4 = 7

(a) Use Euclidean algorithm to find the gcd of 105 and 231.

(b) Use mathematical induction to show that

1 · 1! + 2 · 2! + · · · + n · n! = (n + 1)! − 1

(c) Show that the relation ∼ defined on R as a ∼ b if b−a ∈ Q, is an equivalence relation.

Also, find the equivalence class of 1.

The probabilities that a surgeon operates on 3,4,5,6 or 7 patients in any one day are 0.15, 0.20, 1.25, 0.20, and 0.20, respectively.

In February 2021 1,664,479 persons took the Covid vaccine in Asia the distribution of Pfizer vaccine had a 496 and a 144. Find Z if X =366

Consider the polynomial f(x) = x

5 − 34x

3 + 29x

2 + 212x − 300.

(a) Find upperbounds and lowerbounds for the real roots of f(x).

(b) What are the possible integral roots of f(x)?

(c) Illustrate synthetic division by showing that one of the integers obtained in (b)

is/isn’t a root of f(x).

(d) Illustrate Newton’s method by showing that one of the integers obtained in (b)

is/isn’t a root of f(x)

Children's height are normal with =36 inches and =2 inches So a child 39.5 inches tall has a standardized height of?